NAG Library Routine Document

C06DCF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     X(LX) – REAL (KIND=nag_wp) arrayInput

On entry: $x\in X$, the set of arguments of the series.

Constraint: $\mathbf{XMIN}\le \mathbf{X}\left(\mathit{i}\right)\le \mathbf{XMAX}$, for $\mathit{i}=1,2,\dots ,\mathbf{LX}$.

2:     LX – INTEGERInput

On entry: the number of evaluation points in $X$.

Constraint: $\mathbf{LX}\ge 1$.

3:     XMIN – REAL (KIND=nag_wp)Input

4:     XMAX – REAL (KIND=nag_wp)Input

On entry: the lower and upper end points respectively of the interval $\left[x_{\min },x_{\max }\right]$. The Chebyshev series representation is in terms of the normalized variable $\stackrel{-}{x}$, where

$$\stackrel{-}{x}=\frac{2x-\left(x_{\max }+x_{\min }\right)}{x_{\max }-x_{\min }}\text{.}$$

Constraint: $\mathbf{XMIN}<\mathbf{XMAX}$.

5:     C(N) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{C}\left(\mathit{j}\right)$ must contain the coefficient $c_{\mathit{j}}$ of the Chebyshev series, for $\mathit{j}=1,2,\dots ,n$.

6:     N – INTEGERInput

On entry: $n$, the number of terms in the series.

Constraint: $\mathbf{N}\ge 1$.

7:     S – INTEGERInput

On entry: determines the series (see Section 3).

$\mathbf{S}=1$

The series is general.

$\mathbf{S}=2$

The series is even.

$\mathbf{S}=3$

The series is odd.

Constraint: $\mathbf{S}=1$, $2$ or $3$.

8:     RES(LX) – REAL (KIND=nag_wp) arrayOutput

On exit: the Chebyshev series evaluated at the set of points $X$.

9:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry, $\mathbf{LX}<1$.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{N}<1$.

$\mathbf{IFAIL}=3$

On entry, $\mathbf{S}\ne 1$, $2$ or $3$.

$\mathbf{IFAIL}=4$

On entry, $\mathbf{XMAX}\le \mathbf{XMIN}$.

$\mathbf{IFAIL}=5$

On entry, an element of X is less than XMIN or greater than XMAX.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (c06dcfe.f90)

9.2  Program Data

Program Data (c06dcfe.d)

9.3  Program Results

Program Results (c06dcfe.r)